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Representation Theory

Published by the American Mathematical Society since 1997, this electronic-only journal is devoted to research in representation theory and seeks to maintain a high standard for exposition as well as for mathematical content. All articles are freely available to all readers and with no publishing fees for authors.

ISSN 1088-4165

The 2020 MCQ for Representation Theory is 0.71.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


Generic extensions and multiplicative bases of quantum groups at ${{\mathbf q=0}}$
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by Markus Reineke
Represent. Theory 5 (2001), 147-163
Published electronically: June 12, 2001


We show that the operation of taking generic extensions provides the set of isomorphism classes of representations of a quiver of Dynkin type with a monoid structure. Its monoid ring is isomorphic to the specialization at $q=0$ of Ringel’s Hall algebra. This provides the latter algebra with a multiplicatively closed basis. Using a crystal-type basis for a two-parameter quantum group, this multiplicative basis is related to Lusztig’s canonical basis.
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Bibliographic Information
  • Markus Reineke
  • Affiliation: BUGH Wuppertal, Gaußstr. 20, D-42097 Wuppertal, Germany
  • MR Author ID: 622884
  • Email:
  • Received by editor(s): August 14, 2000
  • Received by editor(s) in revised form: April 10, 2001
  • Published electronically: June 12, 2001
  • © Copyright 2001 American Mathematical Society
  • Journal: Represent. Theory 5 (2001), 147-163
  • MSC (2000): Primary 17B37; Secondary 16G30
  • DOI:
  • MathSciNet review: 1835003